IMPACT OF FOUNDATION MODELING ON THE ACCURACY OF RESPONSE HISTORY ANALYSIS OF A TALL BUILDING Part...

IMPACT OF FOUNDATION MODELING ON THE ACCURACY OF RESPONSE HISTORY ANALYSIS OF A TALL BUILDING

Part II - Implementation

F. Naeim, S. Tileylioglu, A. Alimoradi and J. P. Stewart

Choice of Software (nonlinear capable)

• Commonly used for seismic analysis and design– ETABS– SAP2000– Perfrom-3D

• Public-domain (not user friendly)– OpenSees

• General F.E. (if you are suicidal!)– Adina– Abaqus– Ansys – and more

MA Model

Spring ends constrained to the

ground motion history

Foundation walls modeled with the actual stiffness and strength

Rigid pedestal, free at the bottom and connected to a rigid plate at the top. Vertical and horizontal displacements induced at the bottom.

Vertical nonlinear springs and dashpots connecting the top of rigid plate to the bottom of mat foundation.

Horizontal nonlinear springs and dashpots connected to the basement wall. Horizontal ground displacements are induced at the free end of each spring and dashpot. Note that the same configuration exists at the other end.

Vertical Soil SpringsPedestals

Lateral Soil Springs

Footing for the gravity system

Lateral Soil Springs

Nonlinear ETABS Model (MA)

• Vertical masses included• << Explain the difference between eigen and Ritz

analysis >>• Eigenvalue analysis does not work• 50 Ritz vectors are utilized.

– The first 12 mode shapes used as Ritz vectors– Subbasement deformations used as Ritz vectors

• The gravity load was imposed as a ramp function followed by imposed horizontal and vertical ground displacements

• Damping: 1% critical, except for modes 1 and 4 (1.8%).

0 50 100 150Time (seconds)

Comparison with system identification results

Direction

Identified Periods (sec.)

MA Model Periods (sec.)

Mode 1 Mode 2 Mode 1 Mode 2

E-W 6.07 1.95 6.06 1.92

N-S 5.12 1.86 5.18 1.81

Torsional 2.78 2.76

Period Comparisons

ModelReported vibration periods for first five Ritz vectors (sec.)

1 2 3 4 5

MA* 6.06 5.18 2.76 1.92 1.81

1 6.03 5.15 2.75 1.91 1.81

2A 6.06 5.18 2.76 1.92 1.81

2B 6.06 5.18 2.76 1.92 1.81

2C 6.06 5.18 2.76 1.92 1.81

3A 6.04 5.18 2.78 1.92 1.82

3B 5.79 4.99 2.76 1.92 1.82

3C 5.79 4.99 2.76 1.92 1.82

3D 5.63 4.90 2.74 1.89 1.80

[CSMIP-ID = 24629] - 1994 Northridge Earthquake - Sensor No. 1D

Time (sec)

RecordedMathematical Model

Time (sec)

0 36 72 108 144 180

RecordedMathematical Model(Baseline Corrected)

Time (sec)

0 36 72 108 144 180

RecordedMathematical Model(Baseline Corrected)

Time (sec)

Approximation #3b:Rigid soil beneath base slab and basement wall springs (tension allowed) with fixed ends

INPUT MOTIONS: Free-Field Accelerations applied at the base

Ritz Period Comparison

Mode No. MA Model

App. 3B

1 6.06 5.79

2 5.18 4.99

3 2.76 2.76

4 1.92 1.92

5 1.81 1.82

Time (sec)

0.00 180.01

NOTE: 3B model reports relative displacements. MA results are absolute displacements.

Time (sec)

0.00 180.01

NOTE: 3B model reports relative displacements. MA results are absolute displacements.

Time (sec)

0.00 180.01

Time (sec)

Approximation #3c: Rigid soil beneath base slab and no interaction of soil with basement walls

INPUT MOTIONS: Same as #3d, ug(z=0)

Mode No. MA Model

App. 3C

1 6.06 5.79

2 5.18 4.99

3 2.76 2.76

4 1.92 1.92

5 1.81 1.82

Sensor No. 3D

Time (sec)

Sensor No. 4D

Time (sec)

Sensor No. 6D

Time (sec)

Sensor No. 7D

Time (sec)

Sensor No. 18D

Time (sec)

Sensor No. 19D

Time (sec)

-10 -5 0 5 10Displacement (in.)

-6 -4 -2 0 2 4 6Displacement (in.)

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035Story Drift Ratio

0 0.0005 0.001 0.0015 0.002 0.0025 0.003Story Drift Ratio

Approximation #3d:Embedded portion of structure neglected and fixed base assumed at ground level

INPUT MOTIONS: Free-field ground surface, ug(z=0); f=0

Mode No. MA Model

App. 3D

1 6.06 5.63

2 5.18 4.90

3 2.76 2.74

4 1.92 1.89

5 1.81 1.80

Sensor No. 6D

Time (sec)

Sensor No. 7D

Time (sec)

Sensor No. 18D

Time (sec)

Sensor No. 19D

Time (sec)

0 0.001 0.002 0.003 0.004Story Drift Ratio

Preliminary Findings

• Effects on modal properties are small• Significant effect on drift distribution over

height of structure• Two models do a poor job:

– 3B model: ug applied at base and fixed-end horizontal springs

– 3D model: Fixed base at ground level

• Not so bad (for this building): fixed base at base level of structure

Approximation 3a

Spring ends constrained to the

ground motion history

Tension allowed at soil-foundation interface

Mode No. MA Model

App. 3A

1 6.06 6.04

2 5.18 5.18

3 2.76 2.78

4 1.92 1.92

5 1.81 1.82

Sensor No. 6D

Time (sec)

Sensor No. 7D

Time (sec)

Sensor No. 18D

Time (sec)

Sensor No. 19D

Time (sec)

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035Story Drift Ratio

0 0.0005 0.001 0.0015 0.002 0.0025 0.003Story Drift Ratio

Approximation #1:Rigid Foundation Structural Elements

Spring ends constrained to the ground motion history Foundation walls modeled as

INPUT MOTIONS same as MA

Mode No. MA Model

App. 1

1 6.06 6.04

2 5.18 5.16

3 2.76 2.75

4 1.92 1.91

5 1.81 1.81

Time (sec)

Approximation #2a:No kinematic base rocking

Foundation walls modeled with the actual stiffness and strengthFoundation walls modeled with the actual stiffness and strength

INPUT MOTIONS: same as MA except no vertical motion

Mode No. MA Model

App. 2A

1 6.06 6.06

2 5.18 5.18

3 2.76 2.76

4 1.92 1.92

5 1.81 1.81

121722273237424752

-10 -5 0 5 10

Displacement (in.)

121722273237424752

-6 -4 -2 0 2 4 6

Displacement (in.)

22273237424752

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

Story Drift Ratio

22273237424752

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Story Drift Ratio

Approximation #2b:No kinematic loading from relative soil displacements adjacent to basement walls

INPUT MOTIONS: MA with modification

All horizontal springMotions set equal to the ones at the base

Mode No. MA Model

App. 2B

1 6.06 6.06

2 5.18 5.18

3 2.76 2.76

4 1.92 1.92

5 1.81 1.81

121722273237424752

-8 -6 -4 -2 0 2 4 6 8

Displacement (in.)

121722273237424752

-6 -4 -2 0 2 4 6

Displacement (in.)

22273237424752

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

Story Drift Ratio

22273237424752

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Story Drift Ratio

Approximation #2c No kinematic interaction effects on the base motion

Spring ends constrained to the ground motion history

equivalent free-field horizontal motion

Spring ends constrained to the ground motion history

equivalent free-field horizontal motion

INPUT MOTIONS: Free-field horizontal motions.Taken as ug(z=0) at all levels. No vertical input.

Mode No. MA Model

App. 2C

1 6.06 6.06

2 5.18 5.18

3 2.76 2.76

4 1.92 1.92

5 1.81 1.81

121722273237424752

-10 -5 0 5 10

Displacement (in.)

121722273237424752

-6 -4 -2 0 2 4 6

Displacement (in.)

22273237424752

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

Story Drift Ratio

22273237424752

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Story Drift Ratio

Conclusions

• Soil-structure interaction can affect the response of buildings with subterranean levels

• While procedures are available to account for these effects, they are seldom utilized in engineering practice

• With reasonable tuning of superstructure damping, the MA model accurately reproduces the observed response to the 1994 Northridge earthquake.

• There are hurdles to the implementation of SSI in building design. – Multiple support excitations– Lack of direct integration (ETABS)– Acceleration spikes (ETABS)

• We anticipate these hurdles to go away real soon

Conclusions (continued)

• Factors found to generally have a modest effect on building response above ground level:– compliance of structural foundation

elements– kinematic interaction effects (on translation

or rocking)– depth-variable ground motions applied to

the ends of horizontal soil springs/dashpots.

• However, these factors did generally affect below-ground response as measured by interstory drift

• Properly accounting for foundation/soil deformations does not significantly affect vibration periods for this tall building (which is expected),

• It does impact significantly the distribution of inter-story drifts over the height of the structure.

• To our knowledge, the latter observation is new to this study.

• Two approximations commonly used in practice are shown to provide poor results: 1. fixing the structure at ground line with

input consisting of free-field translation and

2. fixing the structure at the base level, applying free-field motions as input at the base level, and using horizontal foundation springs along basement walls with their end condition fixed to the free-field ground motion.

Thank you!

IMPACT OF FOUNDATION MODELING ON THE ACCURACY OF RESPONSE HISTORY ANALYSIS OF A TALL BUILDING Part...

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